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1 DAVID M. CUTLER Massachusetts Institute of Technology JAMES M. POTERBA Massachusetts Institute of Technology LOUISE M. SHEINER Harvard University LAWRENCE H. SUMMERS Harvard University An Aging Society: Opportunity or Challenge? AN AMERICAN woman reaching childbearing age in 1960 would expect 3.6 children; an identical woman in 1990 would expect only 1.9 children. That dramatic demographic change makes it almost inevitable that the American population will age rapidly over the next 50 years. By 2025, the share of the American population that is 65 or older will exceed the share of Florida's population that is of retirement age today. The ratio of retirees to workers will have risen by nearly two-thirds. Even more dramatic demographic changes are occurring abroad. The share of the Japanese population that is 65 or over will rise from 11 percent to 19 percent over the next two decades. If current fertility levels in West Germany are maintained until 2050, the population will not only age but shrink more than one-third. These demographi changes have aroused considerable anxiety in the United States. Economic concerns have focused on the burden that a We are grateful to George Akerlof, Robert Barro, Greg Duffee, Rachel Friedberg, Ken Judd, Larry Katz, Laurence Kotlikoff, Julio Rotemberg, Robert Solow, and members of the Brookings Panel for helpful comments and to the National Science Foundation and Alfred P. Sloan Foundation for research support. A data appendix for this project is on file at the Inter-university Consortium for Political and Social Research in Ann Arbor, MI. 1

2 2 Brookings Papers on Economic Activity, 1:1990 growing elderly population will place on the economy in general and the federal treasury in particular, as well as on a possible loss of dynamism as population growth slows. Those concerns have led to a potentially radical change in American fiscal policy. To ensure that social security taxes will be sufficient to fund benefits over the next 75 years, and to help the nation save in anticipation of increased demographic burdens, the social security legislation enacted in 1983 calls for social security taxes to exceed benefits over the next 30 years. This surplus will be accumulated in a trust fund, which will peak at 29 percent of GNP in 2020 and then be drawn down as the population ages. This paper steps back from the current political debate over the social security trust fund and examines the more general question of how serious a macroeconomic problem aging is and how policy should respond to it. We focus primarily on issues relating to saving and capital accumulation. We do not consider the broader question of whether the current U.S. national saving rate is too high or too low, but focus on the effect of demographic changes on the optimal level of national saving. In addition, we consider the effects of demographic change on productivity growth and the optimal timing of tax collections. Our general conclusion is that demographic changes will improve American standards of living in the near future, but lower them slightly over the very long term. Other things being equal, the optimal policy response to recent and anticipated demographic changes is almost certainly a reduction rather than an increase in the national saving rate. Slowing population growth will reduce the investment that must be devoted to equipping new workers and housing new families, while making it easier for the United States to attract foreign capital. Although there are many reasons for arguing that the United States currently saves too little, anticipated demographic change is not one of them. Our analysis proceeds in five steps. First, we assess the coming dependency burden. While it is true that the share of the population aged 65 or over will increase sharply, it is also true that the share of children in the population will gradually decline, and that the fraction of the labor force that is near peak productivity will increase. Using information on projected fertility, mortality, and labor force participation rates as well as data on health care costs and the spending of different age groups, we assess past and future dependency trends. We find that demographic changes unaccompanied by changes in capital intensity would reduce

3 D. M. Cutler, J. M. Poterba, L. M. Sheiner, and L. H. Summers 3 per capita incomes by between 7 percent and 12 percent over the next 60 years, but would actually increase incomes over the next 20 years. In only one of the next six decades will demographic changes affect living standards as much as the "peace dividend" is likely to affect them in this decade. The decline in living standards caused by the increased dependence would be fully reversed by a 0.15 percent a year increase in productivity growth. Second, we consider the consequences of the slower labor force growth that presages the increase in the retired share of the population. Between 2010 and 2060, the labor force is expected to decline slightly, compared with an average increase of 1.5 percent annually between 1950 and The projected decline in the labor force growth rate will permit a 3-4 percent reduction in the share of net investment in total income without reducing capital intensity. Since reduced labor force growth will occur before dependency burdens increase, projected demographic changes raise the short-term consumption path even if the steady-state consumption level declines. We show that in a standard growth model with plausible parameter values, optimal consumption typically rises in response to a demographic shock like that experienced in the United States over the past three decades. Third, we consider the implications of integrated world capital markets for our analysis. The degree and speed of population aging in other major industrialized countries, particularly West Germany and Japan, is more dramatic than that in the United States. The increase in dependency abroad will coincide with a deceleration in labor force growth rates. Along an optimal path, therefore, the rest of the world will export capital to the United States-thus increasing U.S. consumption and reducing saving in the short run. Fourth, we go beyond the standard growth theoretic approach and ask whether the coming demographic changes are likely to affect the rate of technical change. With slow labor force growth, labor is scarce; this scarcity may induce more rapid technical change. Such a development would sharpen our conclusion that diminished fertility represents an opportunity rather than a problem. Using international cross-section time series data for , we find some evidence that nations with slower labor force growth do experience more rapid productivity growth. The estimates suggest that the reduction in labor force growth projected for the next 40 years may raise productivity growth enough to offset

4 4 Brookings Papers on Economic Activity, 1:1990 fully the consequences of increased dependence. This finding, however, is uncertain. A more definitive finding is the absence of any empirical support for the pessimistic view that aging societies suffer reduced productivity growth. Fifth, we consider the implications of our findings for fiscal policy. Because demographic changes over the next decades are not likely to be associated with reduced private saving, they constitute no argument for reducing the budget deficit. There remains the question of efficiency in tax collection. Maintaining current service levels for the elderly will require an increase in government spending from about 32 percent to 37 percent of GNP. Since the deadweight loss from taxation rises with the square of the tax rate, financing these expenditures on a pay-as-you-go basis will involve higher deadweight losses than maintaining a constant tax rate. We find, however, that these effects are likely to be small, amounting to at most several tenths of a percent of annual GNP. We conclude by discussing the implications of our results for social security, for intergenerational redistribution more generally, and for population and immigration policy. Our findings suggest that population aging does not constitute a strong argument for accumulating a large social security trust fund, although if national saving is deemed to be inadequate for other reasons, the trust fund may be a convenient way to increase it. The Burden of Increased Dependency The economic consequences of population aging depend on the nature of the underlying demographi change as well as the relationship between the resource needs of individuals at different ages and their capacity for self-support. This section presents our estimates of the economic burden of increased dependency, noting the uncertainties associated with each step in the calculation. Changing Demographic Structure Figure 1 plots the Social Security Administration's projections of the elderly dependency ratio, the number of people aged 65 and over as a fraction of the population aged 20-64, and the total dependency ratio,

5 D. M. Cutler, J. M. Poterba, L. M. Sheiner, and L. H. Summers 5 Figure 1. Actual and Projected Dependency Ratios, United States, a Ratio Sources: Board of Trustees of the Federal Old-Age and Survivors Insurance and the Disability Insurance Trust Funds (1988, table Al, p. 93) and unpublished data from the Social Security Administration underlying the published projections. a. Elderly dependency ratio is the population aged 65 and over divided by the population aged Total dependency ratio is population aged 65 and over plus the population under 20 divided by the population aged

6 6 Brookings Papers on Economic Activity, 1:1990 the number of children plus elderly as a fraction of the working-age population, between 1960 and The figure shows the Social Security Administration's intermediate projections (alternative II) as well as outlying projections making more extreme assumptions about fertility and mortality changes. The projections agree in suggesting that the fraction of the population 65 and over will increase, and the fraction of the population under 20 will decrease, over the next 50 years. There is very little change, however, over the next decade. Declining fertility is the principal source of the changing demographic patterns. ' In stable or declining populations, young cohorts account for a smaller share of the total population than they do in rapidly growing populations. In the years following World War II, the total fertility rate in the United States rose from 2.4 in 1945 to a peak of 3.7 in Fertility declined sharply during the late 1960s and early 1970s, falling to 1.7-well below replacement levels-by Since then, fertility has increased slightly, averaging 1.8 in the mid- 1980s. Preliminary data for 1989 suggest continued increase, to 2.0. These changes have important implications for the demographic structure of the population over the next half-century. The demographic effects of falling fertility have been reinforced by improvements in old-age mortality. In 1960, life expectancy for a 65- year-old man was 12.9 years, compared with 15.0 years in The mortality improvement for women has been even more pronounced, with life expectancy at age 65 increasing from 15.9 to 18.9 years during the past three decades. Current projections call for further improvements in life expectancies at age 65, to 18.0 years for men, and 22.1 years for women, in Long-term demographic projections like those in figure 1 are uncertain for several reasons. First, fertility forecasts are subject to large standard errors and are notoriously inaccurate, as is illustrated by figure 2, which displays historical total fertility rates and the various Social Security Administration projections for the next half-century. The range of historical experience dwarfs the range between the Social Security 1. The relative importance of fertility declines, mortality improvement, and international migration is discussed in OECD (1988). 2. These data are drawn from Board of Trustees of the Federal Old-Age and Survivors Insurance and the Federal Disability Insurance Trust Funds (1990, table 11). More detailed information on mortality improvements can be found in Poterba and Summers (1987).

7 D. M. Cutler, J. M. Poterba, L. M. Sheiner, and L. H. Summers 7 Figure 2. Actual and Alternative Projected Total Fertility Rates, Total fertility rate Source: Projected data are from Board of Trustees of the Federal Old-Age and Survivors Insurance and Disability Insurance Trust Funds (1988, table 11, p. 37). Historical data are from Social Security Area Popuilation Projectionls (1989, pp. 3-4). Administration's optimistic and pessimistic projections. Even the factor of two difference between the predicted share of the population 65 or over in 2050 in the optimistic and pessimistic projections shown in figure 1 probably understates the true degree of demographic uncertainty.3 Postwar fertility projections in the United States anticipated neither the beginning, nor the end, of the baby boom. A second important source of demographic uncertainty is the future course of immigration. The Social Security Administration's intermediate forecasts assume net immigration of 600,000 people a year until 2065-roughly the annual level of net legal and illegal immigration in the late 1980s. Assuming a constant immigrant flow for the next 75 years ignores potential changes in either immigration policy or the level of 3. The pessimistic case assumes an ultimate fertility rate of 1.6, high for example in contrast to West Germany's current rate of 1.3. On the other hand, figure 2 may be deceptive, in that uncertainty regarding the average fertility rate over a 75-year period may be much less than the uncertainty regarding fertility rates at any point in time.

8 8 Brookings Papers on Economic Activity, 1:1990 illegal migration. The age structure of the population is sensitive to the level of immigration because immigrants on average are younger than nonimmigrants. George Boras reports that only 3.1 percent of those who immigrated to the United States between 1975 and 1979 were 65 or over in 1980, compared with 10.6 percent of the nonimmigrant population.4 Higher immigration during the next half-century would reduce dependency burdens. Uncertainty about future mortality gains is a third, but less important, source of randomness in demographic projections. Most of the forecast rise in the number of Americans aged 65 or over is the result of large birth cohorts in the 1950s and 1960s. Even doubling the projected gains in life expectancy at age 65 between 1990 and 2060 would increase the number of elderly in 2060 by less than 20 percent, and change the ratio of the elderly to the working-age population by less than 8 percentage points. Although there is much uncertainty regarding the future age composition of the U.S. population, the broad trend toward a rising average age, a greater number of dependent elderly, and fewer dependent children is indisputable. Moreover, uncertainty about long-term demographic change should not cloud the relatively certain short-term demographic outlook. Labor force growth in the next two decades, for example, is largely forecastable given the fertility experience of the past two decades. Along many dimensions, the near-term effects of demographic change operate in different directions from the long-term changes. To illustrate this we now explore alternative ways to calibrate the shifting burden of demographic change. The Support Ratio Demographic shifts affect the economy's consumption opportunities because they change the relative sizes of the self-supporting and dependent populations. We summarize these changes in the support ratio, denoted a, which we define as the effective labor force, LF, divided by the effective number of consumers, CON: (1) o = LFICON. The share of the population aged 65 and over is one, but not the only, determinant of this ratio. The support ratio is also influenced by the 4. Borjas (1990, pp. 41, 46).

9 D. M. Cutler, J. M. Poterba, L. M. Sheiner, and L. H. Summers 9 relative consumption needs of people of different ages, as well as by changes in the retirement age, labor force participation rates, and the earning power of those who are working. Because there are several approaches to measuring and projecting each of these factors, we present several different measures of the support ratio. The first issue in measuring the support ratio concerns the relative consumption needs of people at different ages. One assumption, which we label CONI, defines effective consumption as if all people have identical resource needs: 99 (2) CONI = Ni, where Ni is the number of people of age i. This measure of needs is implicit in the commonly cited total dependency ratio shown in figure 1. An alternative approach involves differentiating the resource needs of people at different ages. We develop this approach in a second measure of effective consumption needs, CON2, which has three parts: private nonmedical expenses, public education expenses, and medical care. For private nonmedical outlays, we follow Edward Lazear and Robert Michael in assuming that all people 20 and older have identical needs, while those under 20 (18 in their work) have needs equal to onehalf those of adults.' For public education expenses, we assume per capita outlays of $2,553 (1989 dollars) per person under 20, $309 per person aged 20-64, and $84 per person aged 65 and over. These estimates are explained in more detail below. For medical care, we assume that needs are proportional to total spending by age: $1,262 per person per yearforthose under 64 and $5,360for those 65 and over.6 Adding together 5. Lazear and Michael (1980, p. 102) estimate that a child raises equivalent scale consumption for a husband-wife family by 22.2 percent, or by 44.4 percent as much as the average consumption of either parent. There is some evidence that nonmedical consumption needs of the elderly may be lower than those for younger people. For example, the U.S. Department of Agriculture poverty line assumes that food expenditures by the elderly are 90 percent of those for prime-aged individuals. The ongoing trend toward more elderly living in single households, however, suggests that the relative expenditure needs of the elderly may rise in the future. 6. These relative medical costs are based on the current age structure of the elderly population. As the average age of those 65 or over rises, the relative cost of medical care for the elderly will increase. In 1987 total annual per capita health expenditures for people aged were $3,728, compared with $9,178 for those aged 85 and over. Holding agespecific expenditure patterns constant at their 1987 level, average spending per person aged 65 and over would be approximately 10 percent higher with the age composition expected in 2060 rather than that in See Waldo and others (1989).

10 10 Brookings Papers on Economic Activity, 1:1990 these three components, we construct a needs-weighted consumption measure, CON2, as 0.72 times the number of people under 20, plus the number aged 20-64, plus 1.27 times the number 65 and over.7 The relative needs of elderly and nonelderly consumers can be affected by demographic factors such as mortality improvements. Edward Schneider and Jack Guralnik observe that only 3 percent of men and 6 percent of women 65 and over reside in nursing homes, while 15 percent of men and 25 percent of women 85 and over are in such homes. The high cost of nursing home care ($23,600 per resident per year in 1985) makes it an important contributor to the total cost of caring for the aged population.8 The appropriate weighting of young and old dependents may depend on more than their consumption demands. Many of the transfers to children take place within the family, while those to elderly dependents are largely mediated by the government. A Scandinavian proverb, brought to our attention by George Akerlof, suggests that "one mother can care for ten children, but ten children cannot care for one mother." Individuals may derive more pleasure from caring for children than from caring for elderly dependents, making the burdens of an increasingly elderly population more onerous than the burdens of caring for a young population.9 We also consider two different measures of the effective labor force. The first, LF1, assumes that all people aged are in the labor force, while individuals 19 and under or 65 and over are not: 64 (3) LF1 = E Ni. i=20 Our second measure, LF2, recognizes that both human capital and labor force participation rates vary by age. We use data on the average 1989 earnings (w) of people of each age (measured in five-year intervals), 7. The needs-weighted consumption measure, CON2, is defined as 99 CON2 = E Si Ni, i =,I where Si is the respective weight for an individual at age i. 8. Schneider and Guralnik (1990). 9. Provided the "warm glow" of caregiving does not affect the marginal utility of consuming goods, it should not affect our needs weighting of different-aged households. It will affect the total utility of households.

11 D. M. Cutler, J. M. Poterba, L. M. Sheiner, and L. H. Summers 11 along with Social Security Administration forecasts of age-specific labor force participation rates, PR, to estimate LF2: (4) LF2 = E wiprini. i= 15 This recognizes that the earning capacity of a society with a high fraction of people in middle age is higher than that of a society with many new entrants to the labor force. 11 Support Ratio Projections, Because the level of the support ratio is less informative than its changes from year to year, we focus on &'t, the percentage change in the support ratio between 1990 and year t: (5) (Xt = (LFtICONt)I(LF1990ICON190) - 1. We report support ratios corresponding to each combination of effective labor force and effective consumption measures. Table 1 shows the historical and projected changes in LF and CON and demonstrates that regardless of measurement method, growth in both the labor force and consumption requirements declines during the next half-century. For example, the earnings-weighted labor force grew at a 1.7 percent annual rate during the 1980s, but will shrink in four of the five decades between 2010 and In the nearer term, labor force growth also slows. By the first decade of the next century, labor force growth is only one-fourth its rate during the 1970s. Total needs-weighted consumption, which grew at a 1.1 percent annual rate during the 1980s, rises by less than one tenth of 1 percent a year between 2040 and Table 2 and figure 3 show the percentage change in the four alternative measures of the support ratio. Four conclusions stand out. First, because both our measures of the labor force grow more slowly than population 10. These data are from the Bureau of Labor Statistics, Usual Weekly Earnings of Full-Time Wage and Salary Workers and Usual Weekly Earnings of Employed & Part- Time Wage and Salary Workers. We adjust part-time workers to full-time equivalent employees. 11. This labor force concept includes only market activity, neglecting the value of labor devoted to household production. It may therefore overstate the historical changes in the effective labor force that were partly due to rising market labor force participation by women.

12 12 Brookings Papers on Economic Activity, 1:1990 Table 1. Actual and Projected Average Annual Growth in Labor Force and Consumption, United States, Percent Labor force Earnings- Consumption Population weighted Needs population Unweighted weighted Period (LF1) (LF2) (CON1) (CON2) Source: Board of Trustees of the Federal Old-Age and Survivors Insurance and Disability Insurance Trust Funds (1988). Projected data for use alternative Ilb. Data show geometric average annual changes in labor force and consumption needs under IIb. during the next 70 years, there is a long-run decline in the support ratio. The size of the decline is more sensitive to our assumptions about consumption than to our measure of the effective labor force.'2 When consumption needs are assumed to be equal for people of all ages, the support ratio for LFI (LF2) declines by 7.4 percent (7.8 percent) between 1990 and When we adjust consumption using our needs-weighted measure, the decline in the support ratio is more pronounced: 11.5 percent and 11.8 percent for LF1 and LF2, respectively. It is difficult to know whether these estimates represent a large or a small burden spread over 70 years. They correspond to between a 0.10 percent and 0.15 percent reduction in the annual productivity growth rate, which is small relative to the uncertainty in secular productivity growth. They represent three to four times as large a cost as the peace dividend that the United States is likely to enjoy over the next decade. 12. For the period , the support ratios are sensitive to our choice of labor force concept, primarily because of significant changes in labor force participation rates, most notably among women.

13 D. M. Cutler, J. M. Poterba, L. M. Sheiner, and L. H. Summers 13 Table 2. Changes in Support Ratio Relative to 1990, United States, Percent Unweighted Earnings- Unweighted Earnings- population weighted population weighted aged populationl aged populationl needs- needsunweighted unweighted weighted weighted consumption consumption consumption consumption Year (LFIICON1) (LF2/CON1) (LF1/CON2) (LF2/CON2) Source: Same as table 1. The earnings-weighted labor force measure uses contemporaneous and projected labor force participation rates and the 1987 age-earnings profiles for men and women to form effective labor forces. In yet another metric, a three- to four-year increase in the average age at retirement, or a 19 percentage point increase in female labor force participation, would be needed to offset the increase in dependency. Second, in the next two decades there is a decline in economic dependency (a rise in the support ratio) because the declining number of dependent children more than offsets the rising number of dependent elderly. Between 1990 and 2010, when the baby boom generation is part of the labor force and relatively small birth cohorts are retiring, the labor force grows more rapidly than the dependent population. This leads to an improvement in the support ratio by Figure 4 provides further detail on the differential burdens of young and aged dependents. It plots the contributions of both children and the elderly to the support ratio defined using LF2 and CON2. In this case 13. Measures that define effective consumption with less weight on children show smaller gains in the support ratio during the next two decades. If the consumption weight based on needs is set equal to zero for children, the support ratio actually declines by between 1 percent and 2 percent during

14 14 Brookings Papers on Economic Activity, 1:1990 Figure 3. Actual and Projected Changes in Support Ratio (Relative to 1990), Four Alternative Measures, United States, Ratio 1.04 Unweighted population j 1.02 *; Unweighted population aged aged needs-./.'z ' unweighted consumption 1 -weighted '- (LFIICONl) consumption,/: 0.98 (LF1/CON 2)1 4' ,. Earnings-weighted population! ",'.- ~~~~~~~~~needs-weighted consumption 0.84 _'-'.< Eatnings-weightedEpopulation! (LF21CON2) unweighted consumption (LF 2/ CON 1) 0.8 l Source: Table 2. Year = P/(C + P + E), where P is the number of prime-aged adults, C the number of effective children, and E the number of effective elderly. Then the percentage change in the support ratio can be written in terms of the percentage change in its components: (6) = (P - C) [C(C + P + E)] + (P -E) [EI(C + P + E)]. The first term is due to differential growth rates of the prime-aged and dependent children populations, the second to the differential growth between the prime-aged and elderly groups. Figure 4 plots these two terms, showing that virtually all the improvement in the support ratio in the near term is from a shrinking share of children in the population. Most of the long-run decline is a result of rising numbers of elderly during Third, the changes in the support ratio between 1990 and 2060 are usually no larger than, and in some cases significantly smaller than,

15 D. M. Cutler, J. M. Poterba, L. M. Sheiner, and L. H. Summers 15 Figure 4. Contributions of Young and Elderly Dependents to Percentage Changes in the Support Ratio (Relative to 1990), Change in consumption relative to 1990 (percent) 4% ~~ " a ~~ A X a~~~~~~~~~~ Tota change -8 t \ e ~ ~~~~Sha-e of eldet-iya, \ -10lo. - Shat-e of childi-en' -12 _ -...s X l l l l l l l l l l l l l l l l l l l Year Source: Authors' calculations using equation 6. The earnings-weighted labor force measure (LF2) and the needsweighted consumption measure (CON2) are used. See text for details. those between 1960 and With our preferred measures, LF2 and CON2, the support ratio was 14.0 percent lower in 1970 than By 2060, it is projected once again to be below the 1990 level, this time by 11.8 percent. Our support ratio peaks around One reason why the slow growth of real wages in the U.S. economy since 1973 has been less burdensome than it might have otherwise been is that the labor force participation rate has risen. The figures show clearly that the gains in sustainable consumption from demographic developments are now nearly exhausted. Finally, while the decline in the support ratio by the middle of the next century is large, there is still substantial uncertainty about the ultimate burden. Figure 5 presents support ratios using LF2 and CON2 under the three Social Security Administration demographic forecasts. There are substantial differences in the scenarios, particularly between the more pessimistic alternative III and alternative II, which is our

16 16 Brookings Papers on Economic Activity, 1:1990 Figure 5. Percentage Change in Support Ratio (Relative to 1990), Alternative Demographic Assumptions, Index relative to \- lesntv -18 a 0 l l i i* -16 AlternativeIII iv Year Source: Authors' calculations using Board of Trustees of the Federal Old-Age and Survivors Insurance and Disability Insurance Trust Funds (1988) and the needs-weighted consumption (CON2) and earnings-weighted labor force (LF2) measures. standard case. The decline in the support ratio is almost twice as large in the pessimistic scenario as in our benchmark. Even in the optimistic alternative I, the support ratio still declines by almost 8 percent between 1990 and Capital Accumulation and Shifting Dependency Burdens This section explores how the demographic shifts described above affect the economy's sustainable level of consumption, and how society should plan for these changes. We find that sustainable consumption increases for the next several decades and that an economy with otherwise optimal national saving would reduce its saving in response to the coming demographic changes.

17 D. M. Cutler, J. M. Poterba, L. M. Sheiner, and L. H. Summers 17 Steady-State Consumption Opportunities Demographic change has two effects on consumption opportunities. First, an increase in dependency lowers output per person, thus reducing consumption per capita. Second, slower labor force growth reduces investment requirements, thus reducing the need for saving and increasing consumption per capita. To examine the importance of these two changes for consumption opportunities, we assume that output per worker, f(k), where k is the capital-labor ratio, is divided between consumption and investment. Maintaining constant capital intensity requires investment of nk, where n is the labor force growth rate. 14 For expositional ease, we have assumed away depreciation and technical change. '5 When the labor force and the population are not the same, consumption per capita is only a fraction of output net of investment per worker. This fraction is the ratio of the number of workers to the size of the population, precisely the support ratio (o) defined above. The resulting equation for per capita consumption is: (7) c = ot(k) - nk]. This expression can be rewritten to find the change in steady-state consumption for changes in a and n: (8) Aclc = Ao/ot - [o(klc) An + Aot (klc) An], with c, k, and a evaluated at the initial steady state.16 Equation 8 illustrates the two steady-state effects of demographi change. A decline in the labor force-population ratio (o) reduces the level of per capita consumption that is feasible given the economy's capital stock. At the same time, a decline in the growth rate of the labor force (n) permits more consumption for a given capital-output ratio. Society receives a "consumption dividend" when it is able to invest less and still maintain 14. A substantial part of the U.S. capital stock is residential capital. The natural steadystate condition for housing requires investment at the rate of population growth, not the rate of labor force growth. In steady state, these two growth rates will coincide. 15. We incorporate both in our numerical simulations below. 16. We have arbitrarily assigned the second-order term to the second effect in our decomposition. We have also assumed that the capital-labo ratio, and thus the capitalconsumption ratio, do not change with demographichange. The model we present below justifies this assumption.

18 18 Brookings Papers on Economic Activity, 1:1990 Table 3. Shifting Steady-State Per Capita Consumption from Demographic Shocks, a Percent Unweighted consumption (CON1) Needs-weighted consumption (CON2) Total Total Effect of change in per capita Effect of change in per capita Year Effect of labor force consump- Effect of labor force consumpdependency growth tion dependency growth tion Population as effective laborforce (LF1) Earnzings-weighted labor force (LF2) Source: Authors' calculations. a. The table shows the steady-state change in consumption relative to the 1990 base if demographichange were to reach a steady state at the level of the indicated year. a given level of per capita output. This "Solow effect" offsets the longrun dependency effect on per capita consumption. Table 3 reports the size of these two effects. For each year, we show the steady-state consumption change associated with changes in a (first column), n (second column), and the combined effect (third column). The consumption changes due to the dependency increase are the same

19 D. M. Cutler, J. M. Poterba, L. M. Sheiner, and L. H. Summers 19 as the changes in the support ratio shown in table 2; the other columns show the extent to which changing investment needs offset this effect. Two results emerge from table 3. First, the consumption benefits from reduced investment requirements are substantial. During the next two decades, the benefits of slower labor force growth will be about a 1 percent to 3.5 percent increase in per capita consumption, using the 1990 base. Since the labor force was growing more rapidly in the 1970s and 1980s than in 1990, the effect of reduced investment requirements is even larger relative to earlier years. By the middle of the next century, the benefits of slower labor force growth will be between 2.1 percent and 3.7 percent of per capita consumption. This is between one-quarter and one-half of the adverse dependency effects of the changing population mix. Second, while the investment effect offsets a substantial part of the long-term dependency increase, it magnifies the short-run effect of rising support ratios. Reduced dependency and slowing labor force growth both increase consumption possibilities so that by 2010, society will be between 3.4 percent and 6.3 percent richer, depending on the combination of labor force and needs measures. Only after 2020 does the increase in dependency outweigh the decline in investment needs and reduce consumption below its 1990 level. The steady-state consumption decline between 1990 and 2060 is estimated at between 4.2 percent (with effective consumers set equal to total population and the earnings-weighted labor force) and 9.4 percent (with effective consumers computed using our needs-weighted measure and the unweighted labor force). As with the support ratios, this finding is more sensitive to our definition of consumption needs than to our definition of the effective labor force. For almost all cases, however, society is richer in the new steady state than in 1970 or Demographic Change and Optimal Capital Accumulation The results presented so far suggest that in the short run, demographic changes will raise the level of consumption that can be sustained while maintaining the level of capital intensity. In the long run, they will reduce the sustainable level of consumption. The question then becomes how society should adjust its saving policy to these developments. To study this question, we use the standard Ramsey optimal growth model.

20 20 Brookings Papers on Economic Activity, 1:1990 We assume that a social planner seeks to maximize (9) V = f e-pipt U(ct)dt, where Pt denotes the number of individuals alive in period t, ct is per capita consumption in period t, and p is the social time preference rate. We denote the current period as time zero. This social welfare function weights the utility, denoted as U, of a representative individual in each generation by the generation's size.'7 Using our earlier notation, Pt = Ntlot, where Nt is the labor force in period t and ot is the support ratio. Our analysis abstracts from the overlapping generations structure of the actual population. Calvo and Obstfeld formally justify this procedure by demonstrating that if age-specific transfer programs like social security are available, and if individual utility functions are additively separable, then "the Cass-Koopmans-Ramsey framework can be used to evaluate paths of aggregate consumption even in models where different generations co-exist.... the planning problem facing the government can be decomposed into two subproblems, a standard problem of optimal aggregate capital accumulation and a problem of distributing consumption optimally on each date among the generations alive then." 18 The social planner maximizes equation 9 subject to a capital accumulation constraint analogous to equation 7:19 (10) kt =f(kt) - ctiot - ntikt. If at = 1, equation 10 reduces to the standard resource constraint in neoclassical growth models. The consumption profile that solves this problem satisfies: (11) &tict = u[ f'(kt) - P] where u = [- sumption. U'(ct)Ict] [U"(ct)], the elasticity of substitution in con- 17. Some might argue for using an alternative objective function that does not weight the average utility of different generations by the number of people in the generation. This will lead the social planner to raise average consumption in small cohorts relative to that in larger cohorts, because the aggregate resource cost of raising the average consumption of people in small cohorts is less than that for large cohorts. We see no compelling ethical argument for weighting people in different sized cohorts differently. 18. Calvo and Obstfeld (1988, p. 163). 19. The optimal plan must also satisfy transversality conditions noted for example by Blanchard and Fischer (1989).

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